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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.03617 |
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| _version_ | 1866912521619767296 |
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| author | Richardson, Robert Tolley, H. Dennis Kuttler, Kenneth |
| author_facet | Richardson, Robert Tolley, H. Dennis Kuttler, Kenneth |
| contents | We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation to flexibly model skewness, heavy tails, and other non-Gaussian features often observed in real data. We rigorously define the process, establish key probabilistic properties, and construct a corresponding diffusion model via stochastic calculus, including proofs of existence and uniqueness. A simplified approximation is introduced and analyzed, with error bounds derived from asymptotic expansions. Simulations demonstrate that both the full and simplified models recover target marginals with high accuracy. Examples using the Student's t, asymmetric Laplace, and Exponentialized Generalized Beta of the Second Kind (EGB2) distributions illustrate the flexibility and tractability of the framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03617 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expanding the Standard Diffusion Process to Specified Non-Gaussian Marginal Distributions Richardson, Robert Tolley, H. Dennis Kuttler, Kenneth Statistics Theory We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation to flexibly model skewness, heavy tails, and other non-Gaussian features often observed in real data. We rigorously define the process, establish key probabilistic properties, and construct a corresponding diffusion model via stochastic calculus, including proofs of existence and uniqueness. A simplified approximation is introduced and analyzed, with error bounds derived from asymptotic expansions. Simulations demonstrate that both the full and simplified models recover target marginals with high accuracy. Examples using the Student's t, asymmetric Laplace, and Exponentialized Generalized Beta of the Second Kind (EGB2) distributions illustrate the flexibility and tractability of the framework. |
| title | Expanding the Standard Diffusion Process to Specified Non-Gaussian Marginal Distributions |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2508.03617 |